How can I bevel an object gradually?
It is hard to do it accurately in Blender, but you could approximate the result using the help of Proportional Edit



Just bevel regularly like you already did, but make sure you leave the 3D Cursor at the exact position of the original unbeveled corner vertex on 1.

If you already beveled you can place a loose vertex there and use the Shift+S menu then Cursor to Selected to snap it there.

Afterwards hide all geometry of your object by selecting it and pressing H (so it doesn't get unintentionally deformed), except for the beveled edges only.

Turn on Proportional Edit (O key by default), set Falloff Type to Linear then selecting only the tip vertex at 1 scale down as desired. Press Shift+X (Y or Z depending on the orientation of your model) to exclude the desired axis from scaling and prevent distortions, then adjust the influence radius with Mousewheel as desired.

In the end Alt+H to unhide hidden geometry